1. Field of the Invention
The present invention relates generally to a method of precisely correcting geometrically distorted satellite images, and more particularly to a method of precisely correcting geometrically distorted satellite images, which measures position and attitude values of a satellite by separating variables having a high correlation therebetween, and which precisely corrects geometrically distorted satellite images using the position and attitude values of the satellite. In addition, the present invention relates to a computer-readable storage medium in which a program for executing the satellite image correcting method with a computer is stored.
2. Description of the Prior Art
Generally, remote sensing data obtained by an artificial satellite or the like may include many errors and distortions according to equipment allowances and atmospheric conditions at the time of observation, the trajectory and photographing position and attitude of a photographing satellite, the curvature and rotation of the earth, etc. Technologies for correcting geometrically distorted satellite images are very important in application fields, such as precise map production, multi-temporal image applications, and remote sensing applications.
Satellite image data including errors and distortions are designated as geometrically distorted satellite images. Such a geometrical distortion can be corrected by geometrically modeling the position of a satellite as shown by the dashed line FIG. 1, the photographing angle of a sensor, the curvature and rotating speed of the earth, etc. Such a geometric distortion correcting method is designated as geometric correction. However, even after the geometric correction is carried out, a remaining error (a difference between an actual ground control point and a corrected ground control point) still exists. The reason for existence of the remaining error is that the determination of the position and attitude of the satellite when the satellite image is photographed is inaccurate.
Therefore, ground control points are extracted from the satellite image, and the position and attitude of the satellite at the time of photographing are obtained using the extracted ground control points, such that the remaining error is eliminated. This process is called precision geometric correction. In this case, the ground control points are coordinates obtained by extracting points, having the same shape in both the satellite image and a reference map, from the satellite image so as to allow the satellite image to correspond to the reference map.
As described above, in order to precisely correct the satellite image, more accurate position and attitude values of the satellite must be obtained. The position and attitude values of the satellite have a high correlation therebetween. This means that the position and attitude values are related to each other, so the variation of one of them influences the other.
Due to the correlation between the position and attitude values of the satellite, it is impossible to accurately estimate position and attitude values using a typical least square method. In the prior art, the correlation therebetween is completely ignored, or a part of variables are set to constants and a plurality of ground control points are used, such that the satellite image is precisely corrected. Therefore, if plural accurate ground control points are used, the remaining error can be reduced, but accurate position and attitude values of the satellite cannot be obtained. In this case, the position and attitude values of the satellite, which are previously obtained, cannot be utilized for precision correction of another satellite image adjacent to the satellite image. Further, precision correction cannot be carried out for a satellite image obtained by photographing an area from which ground control points cannot be extracted.
FIG. 1 illustrates a geometric relationship between image coordinates (x, y) of a satellite image photographed by a camera and coordinates (X, Y, Z) of a ground control point “A”. The camera photographs a three-dimensional photographing area as a two-dimensional image, so the coordinates (x, y) of the photographed satellite image and the ground control point (X, Y, Z) have a certain relation. However, since the satellite image is geometrically distorted, a remaining error ε exists between actual coordinates (x, y) corresponding to an arbitrary ground control point and calculated coordinates (x′, y′) from the geometric modeling. Hereinafter, a method of correcting the remaining error of the satellite image is described in detail.
First, there is set a model that represents a geometric relationship between a reference coordinate system of a camera sensor of a satellite at the time of photographing a satellite image and a reference ground coordinate system of a photographed area (photographed ground surface), or between image coordinates (x, y) and a ground control point A (X, Y, Z). In this case, a geometric model of a linear pushbroom sensor is used as an example. The geometric model of the linear pushbroom sensor is expressed by the following collinearity Equations [1] and [2],
                    x        =                                            -              f                        ⁢                                                  ⁢                                                                                r                    11                                    ⁢                                      (                                          X                      -                                              X                        s                                                              )                                                  +                                                      r                    21                                    ⁡                                      (                                          Y                      -                                              Y                        s                                                              )                                                  +                                                      r                    31                                    ⁡                                      (                                          Z                      -                                              Z                        s                                                              )                                                                                                                    r                    13                                    ⁡                                      (                                          X                      -                                              X                        s                                                              )                                                  +                                                      r                    23                                    ⁡                                      (                                          Y                      -                                              Y                        s                                                              )                                                  +                                                      r                    33                                    ⁡                                      (                                          Z                      -                                              Z                        s                                                              )                                                                                =          0                                    [        1        ]                                y        =                              -            f                    ⁢                                          ⁢                                                                      r                  12                                ⁢                                  (                                      X                    -                                          X                      s                                                        )                                            +                                                r                  22                                ⁡                                  (                                      Y                    -                                          Y                      s                                                        )                                            +                                                r                  32                                ⁡                                  (                                      Z                    -                                          Z                      s                                                        )                                                                                                      r                  13                                ⁡                                  (                                      X                    -                                          X                      s                                                        )                                            +                                                r                  23                                ⁡                                  (                                      Y                    -                                          Y                      s                                                        )                                            +                                                r                  33                                ⁡                                  (                                      Z                    -                                          Z                      s                                                        )                                                                                        [        2        ]            
where f is a focal length of the camera, and (Xs, Ys, Zs) are focal positions of the linear pushbroom sensor and (X, Y, Z) is coordinate of a ground control point. In this case, the focal positions of the linear pushbroom sensor correspond to desired position values of the satellite. Further, r11 to r33 are elements of a matrix R for rotating a coordinate system of the linear pushbroom sensor so as to allow the linear pushbroom sensor coordinate system to correspond to a ground coordinate system, and the matrix R is expressed by the following Equation [3],
                    R        =                  (                                                                      cos                  ⁢                                                                          ⁢                  ϕ                  ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                  κ                                                                                                  -                    cos                                    ⁢                                                                          ⁢                  ϕ                  ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                  κ                                                                              sin                  ⁢                                                                          ⁢                  ϕ                                                                                                                          sin                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    ϕcos                    ⁢                                                                                  ⁢                    κ                                    +                                      cos                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    κ                                                                                                                                          -                      sin                                        ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    ϕsin                    ⁢                                                                                  ⁢                    κ                                    +                                      cos                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    κ                                                                                                                    -                    sin                                    ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                  ϕ                                                                                                                                                -                      cos                                        ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    ϕ                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    κ                                    +                                      sin                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    κ                                                                                                                    cos                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    ϕ                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    κ                                    +                                      sin                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    κ                                                                                                cos                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                  ϕ                                                              )                                    [        3        ]            
[3] where κ, φ and ω are rotating angles at which the linear pushbroom sensor coordinate system is rotated around Z, Y and X axes of the satellite coordinate system, respectively, so as to allow the linear pushbroom sensor coordinate system to correspond to the ground coordinate system. Unlike a perspective projection sensor, the linear pushbroom sensor is designed such that its focal positions are determined depending upon lines or parts of a satellite image, and its attitude can vary depending upon lines or parts thereof. Therefore, the focal position values (Xs, Ys, Zs) of the linear pushbroom sensor in Equations [1] and [2], and the rotating angles κ, φ and ω thereof can be represented by linear or non-linear polynomial expressions for an image coordinate value x according to a photographing manner or a scanning manner of the linear pushbroom sensor. In this case, κ, φ and ω are desired attitude values of the satellite to be obtained.
As described above, in the collinearity Equations expressed in Equations [1] and [2], the satellite photographs an image while moving along a direction of its movement, so the focal positions of the linear pushbroom sensor, that is, position values (Xs, Ys, Zs) of the satellite, and the elements r11 to r33 of the rotation matrix R are expressed as functions of time, not as constants. In the prior art, the position values (Xs, Ys, Zs) and the attitude values (κ, φ and ω) of the satellite are modeled as quadratic equations of time as indicated in the following Equation [4].
                                                                        X                z                            =                                                X                  0                                +                                                      a                    1                                    ⁢                  t                                +                                                      b                    1                                    ⁢                                      t                    2                                                                                                                          Y                z                            =                                                Y                  0                                +                                                      a                    2                                    ⁢                  t                                +                                                      b                    2                                    ⁢                                      t                    2                                                                                                                                          Z                z                            =                                                Z                  0                                +                                                      a                    3                                    ⁢                  t                                +                                                      b                    3                                    ⁢                                      t                    2                                                                                                                          κ                z                            =                                                κ                  0                                +                                                      a                    4                                    ⁢                  t                                +                                                      b                    4                                    ⁢                                      t                    2                                                                                                                                          ϕ                z                            =                                                ϕ                  0                                +                                                      a                    5                                    ⁢                  t                                +                                                      b                    5                                    ⁢                                      t                    2                                                                                                                          ω                s                            =                                                ω                  0                                +                                                      a                    6                                    ⁢                  t                                +                                                      b                    6                                    ⁢                                      t                    2                                                                                                          [        4        ]            
In order to obtain the position and attitude of the satellite in the prior art, φ and ω are assumed to be constants, and quadratic equations of the remaining four variables are applied to the collinearity equations, a linearizing operation is carried out using Taylor's theorem, and unknown values, such as X0, Y0, Z0, κ0, a1, a2, a3, a4, b1, b2, b3, and b4, are obtained. Further, using the obtained unknown values, a geometrically distorted satellite image is precisely corrected. In this case, the reason for assuming the functions of time φ and ω to be constants is that a high correlation exists between the functions φ and ω and the position variables of the satellite.
In this way, variables having high correlation are assumed to be constants and equations are solved in the prior art. In this case, if many ground control points are used, the remaining error of the satellite image can be reduced, but accurate position and attitude information of the satellite cannot be obtained.
Generally, if accurate position and attitude information of a satellite is obtained for a satellite image, more accurate position and attitude information of the satellite can be obtained for a satellite image adjacent to the processed satellite image by interpolation. However, in the prior art, accurate position and attitude information of the satellite cannot be obtained, so the obtained position and attitude information cannot be utilized for precision correction of the adjacent satellite image.